Multi-bit Decentralized Detection of a Weak Signal in Wireless Sensor Networks with a Rao test

We consider decentralized detection (DD) of an unknown signal corrupted by zero-mean unimodal noise via wireless sensor networks (WSNs). To cope with energy and/or bandwidth constraints, we assume that sensors adopt multilevel quantization. The data are then transmitted through binary symmetric channels to a fusion center (FC), where a Rao test is proposed as a simpler alternative to the generalized likelihood ratio test (GLRT). The asymptotic performance analysis of the multi-bit Rao test is provided and exploited to propose a (signal-independent) quantizer design. Numerical results show the effectiveness of Rao test in comparison to GLRT and the performance gain obtained by threshold optimization.